General relativity predicts the existence of gravitational singularities at the classical level: our universe started with the big bang, and massive stars can collapse into black holes. A theory that describes quantum gravitational effects should elucidate our understanding of these singularities. The existence of these singularities also raises the question whether propagation of quantum fields through a singularity is possible (and how it should be formulated). String theory can already deal with some timelike singularities but not yet with spacelike singularities like the big bang. Near singularities, strings often interact strongly. A formulation of string theory that allows to take strong interactions between strings into account is given by matrix theory. Matrix theory models that describe singularities often have a dual translation in terms of a quantum field theory that is defined on a singular background spacetime. In this dissertation we investigate these issues. We use a geometric regularization prescription to define the evolution of a free scalar field and of a free string through a singularity in an unambiguous manner. Remarkably, this geometric regularization seems to reveal there is a certain feature of discreteness related to the evolution across the singularity. We also consider an important class of time-dependent backgrounds that can be investigated in string theory. This class is called gravitational plane waves. These plane waves can be used to investiga

presented in Chap. 28. 410.2 Black Holes Quantum field theory predicts that, near the horizon of a black … and to quantization of black holes. Indeed, the thermal properties of black holes, and most especially … as black hole is formed genericity of singularities inside black holes Exercise 26.11 Example: Rindler

Trous noirs et solutions régulières en théorie des cordes Il existe des nombreuses solutions lisses dans le domaine de la théorie des cordes, caractérisées par une topologie non triviale (bulles) et sans sources localisées. Dans cette thèse nous analysons quelques-unes parmi les solutions les plus importantes avec les différents objectifs pour lesquels ils sont étudiés. Des solutions lisses en onze dimensions peuvent être interprétées comme microétats BPS de trou noir dans le cadre de la Fuzzball proposal. On peut promouvoir ces microétats à être quasi-BPS en plaçant de supertubes au minimum métastable à l’intérieur de ces solutions. Nous montrons que ces minima peuvent abaisser leur énergie lorsque les bulles se déplacent dans certaines directions dans l’espace des modules, ce qui implique que ces microétats quasi-BPS sont en fait instables. L’énergie dissipée par ces solutions correspond au rayonnement Hawking et on compare le taux d’émission et la fréquence à celles du trou noir correspondant. En modifiant la géométrie asymptotique de ces microétats on pourrait construire des microétats pour des trous noirs BPS sans charge électrique en cinq dimensions. Il faut donc trouver une nouvelle solution de supergravité en cinq dimensions dont la norme du vecteur de Killing passe de positive à nulle dans certaines régions. Nous construisons des exemples explicites où la norme du vecteur de Killing supersymétrique est une fonction réelle non-analytique telle que tous ses dérivés sont nulles à un point où le vecteur de Killing devient nul. Dans la solution de Lin-Lunin-Maldacena on trouve un mécanisme pour briser la supersymétrie similaire à celui utilisé pour les microétats quasi-BPS. Nous analysons l’énergie potentielle de branes M2 polarisés en branes M5. Lorsque les charges des M2 sont parallèles à ceux de la solution, nous trouvons des configurations stables. Lorsque les charges des M2 ne sont pas parallèles, nous trouvons des états métastables qui brisent la supersymétrie et nous analysons le processus de rayonnement d’énergie. Nous analysons aussi la solution de Klebanov-Strassler et construisons sa version T- duale dans la supergravité de type IIA. Pour cela une analyse approfondie est nécessaire pour choisir l’isomérie la plus appropriée. Notre construction est la première étape d’un programme pour tester la stabilité des antibranes dans la supergravité de type IIA.

General relativity posits that spacetime is not a xed structure but that it is represented by a dynamical metric eld. The gravitational attraction between matter appears as follows: the dynamics of the metric eld is related to the distribution of matter throughout the universe, and the propagation of matter through spacetime is in uenced by the metric eld that represents the universe. After the discovery that matter particles and microscopic forces obey quantum mechanical laws, it has thus become necessary to quantize the metric eld as well. One of the research lines for a consistent theory of quantum gravity has led to string theory. String theory describes the gravitational interaction in terms of gravitons, which are the quanta of the gravitational force. In string theory it is assumed that at the smallest scales elementary particles have a stringlike nature instead of a pointlike nature. But the behaviour of strings on time-dependent backgrounds such as our expanding universe is not well understood yet. General relativity predicts the existence of gravitational singularities at the classical level: our universe started with the big bang, and massive stars can collapse into black holes. A theory that describes quantum gravitational effects should elucidate our understanding of these singularities. The existence of these singularities also raises the question whether propagation of quantum elds through a singularity is possible (and how it should be formulated). String theo

gravitational singularities inside black holes, the ad hoc postulation of dark matter, as well as dark energy and its relation to the cosmological constant Quantum gravity (QG) is a field of theoretical physics that seeks unification of the theory of gravity with the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang. Three Quantum gravity (QG) is a field of theoretical physics that seeks unification of the theory of gravity with the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang. Three of the four fundamental interactions of nature are described within the framework of quantum mechanics and quantum field theory: the electromagnetic interaction, the strong interaction, and the weak interaction; this leaves gravity as the only interaction that has not been fully accommodated. The current understanding of gravity is based on Albert Einstein's general theory of relativity, which incorporates his theory of special relativity and deeply modifies the understanding of concepts like time and space. Although general relativity is highly regarded for its elegance and accuracy, it has limitations: the gravitational singularities inside black holes, the ad hoc postulation of dark matter, as well as dark energy and its relation to the cosmological constant are among the current unsolved mysteries regarding gravity, all of which signal the collapse of the general theory of relativity at different scales and highlight the need for a gravitational theory that goes into the quantum realm. At distances close to the Planck length, like those near the center of a black hole, quantum fluctuations of spacetime are expected to play an important role. Finally, the discrepancies between the predicted value for the vacuum energy and the observed values (which, depending on considerations, can be of 60 or 120 orders of magnitude) highlight the necessity for a quantum theory of gravity. The field of quantum gravity is actively developing, and theorists are exploring a variety of approaches to the problem of quantum gravity, the most popular being M-theory and loop quantum gravity. All of these approaches aim to describe the quantum behavior of the gravitational field, which does not necessarily include unifying all fundamental interactions into a single mathematical framework.…